What is a ?non-constructive proof??

José Manuel Rodríguez Caballero josephcmac at gmail.com
Wed Feb 19 09:52:32 EST 2020

JS wrote:
> There are at least three kinds of ?non-constructive proofs? that I have
> seen:
> (1) A theorem that certain equations have finitely many solutions, with no
> bound given that would allow one to exhaustively search for them
> (2) A theorem that a certain equation has a solution, with no bound given,
> but a guarantee that searching will eventually find one
> (3) A counting argument that an object with certain properties of a
> certain size must exist, which comes with an implicit exponential bound on
> the search but no efficient construction.

I do not see how Goodstein theorem, which is the prototypical example of a
non-constructive result, fits into this classification.

Kind regards,
Jose M.
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